D-STAG: A Formalism for Discourse Analysis Based on SDRT ...

D-STAG: A Formalism for Discourse Analysis

Based on SDRT and Using Synchronous TAG

Laurence Danlos

Universite Paris Diderot, IUF, [email protected]

Abstract. d-stag is a new formalism for the automatic analysis ofdiscourse. It computes hierarchical discourse structures annotated withdiscourse relations. They are compatible with those computed in sdrt.A discursive stag grammar pairs up trees anchored by discourse con-nectives with trees anchored by (functors associated with) discourserelations.

1 Introduction

The aim of this paper1 is to propose a new formalism for the automatic analysisof texts, called d-stag for Discourse Synchronous tag. This formalism extendsa sentential syntactic and semantic analyzer to the discursive level: a discursiveanalyzer computes the “discourse structure” of the input text. Discourse struc-tures consist of “discourse relations” (also called “rhetorical relations”) that linktogether discourse segments — or more accurately, the meanings these discoursesegments convey. A discourse is coherent just in case every proposition that is in-troduced in the discourse is rhetorically connected to another bit of information,resulting in a connected structure for the whole discourse.

For the discursive part of our analyzer, we rely on sdrt — Segmented Dis-course Representation Theory [1,2]. d-stag computes discourse structures whichare compatible with those produced in sdrt. Therefore, d-stag can take advan-tage of the results brought by this discourse theory.

The research done in the framework of sdrt is theory-oriented, providing for-mally detailed accounts of various phenomena pertaining to discourse. Much lessfocus has been put on the issue of implementing a robust and efficient discourseanalyzer. For this aspect of the work, we have designed a formalism based ontag – Tree Adjoining Grammar [12]. After being used successfully for syntacticanalysis in various languages, tag has been extended in two directions: movingfrom sentential syntactic analysis to semantic analysis — with, among others,stag [21,22,17] —, and moving from the sentence level to the discourse level,both for text generation — with, among others, g-tag [5] —, and for discourseparsing — with, among others, d-ltag [10]. The new formalism presented here

1 A (longer) French version of this paper is published in Revue TAL, Volume 50,Numero 1, 2009, pp 111-143.

P. de Groote, M. Egg, and L. Kallmeyer (Eds.): FG 2009, LNAI 5591, pp. 64–84, 2011.c© Springer-Verlag Berlin Heidelberg 2011

D-STAG: A Formalism for Discourse Analysis 65

relies on all this previous work. In particular, its architecture is inspired fromthat of d-ltag, with three components:

1. a sentential analyzer, which provides the syntactic and semantic analyses ofeach sentence in the discourse given as input,

2. a sentence-discourse interface, which is a mandatory component if one wantsnot to make any change to the sentential analyzer,

3. a discursive analyzer, which computes the discourse structure.

This paper is organized as follows. Section 2 presents the main discursive linguis-tic data that motivate d-stag. Section 3 gives an introduction to stag. Section 4briefly describes the sentence-discourse interface. Section 5 explains in detail thediscursive analyzer. Section 6 compares d-stag and d-ltag.

2 Discursive Linguistic Data

A discourse relation is often explicitly expressed by a “discourse connective”.The set of discourse connectives includes subordinating and coordinating con-junctions (because, or) and discourse adverbials (next, therefore). Connectivescan be ambiguous. For example, then lexicalizes the relation Narration in anarrative (Fred went to the supermarket. Then, he went to the movies.) whereasit lexicalizes Continuation in an enumeration ( . . . The second chapter presentsa state of the art. Then, the third chapter explains the problematics.). Discourserelations need not be explicitly marked. For example, the relation Explanationin the connective-free discourse Fred fell. Max tripped him up. of the form C0. C1.must be inferred from (extra)linguistic knowledge. For such a case, we assumethe existence of an empty adverbial connective, noted ε, following a propositionmade in [11]. So the previous discourse is assumed to be of the form C0. ε C1.,and we say, although somewhat inaccurately, that ε lexicalizes Explanation.In a nutshell, a discourse relation can be considered as a semantic predicatewith two arguments which is lexicalized by a discourse connective (possiblyempty) with two arguments. The arguments of a discourse relation/connectiveare the discursive semantic/syntactic representations of the same (continuous)discourse segments. These are the basic principles on which our stag discursivegrammar relies.

One should wonder what discourse structures correspond to when representedas dependency graphs (in which a predicate dominates its arguments). The ideais widespread that dependency graphs representing discourse structures are tree-shaped: this is a basic principle in rst — Rhetorical Structure Theory [14,15]—, a theory on which many text generation or parsing systems have been basedfor the last twenty years. This is also a principle which guided the conception ofd-ltag. Yet this tree-shaped structure is more a myth than a reality, as shownin [24] and in some of our previous work [6,7]. sdrt discourse structures are notrepresented as dependency graphs, however, in our two aforementioned papersand in this one, we convert sdrt discourse structures into dependency graphs.These dependency graphs are dags — Directed Acyclic Graphs — which are not

66 L. Danlos

necessarily tree-shaped. However, these dags respect strong constraints whichrule out a number of dags that don’t correspond to any discourse structure. Weshall justify this claim with discourses of the form C0 because C1. Adv2 C2., inwhich because lexicalizes Explanation; Ci symbolizes the ith clause, its logicalform is noted Fi. These discourses yield four types of interpretation — but nomore than four — which are illustrated in examples (1).2

(1) a. Fred is in a bad mood because he lost his keys. Moreover, he failed hisexam.

b. Fred is in a bad mood because he didn’t sleep well. He had nightmares.c. Fred went to the supermarket because his fridge is empty. Then, he went

to the movies.d. Fred is upset because his wife is abroad for a week. This shows that he

does love her.

In (1a), Adv2 = moreover lexicalizes the relationContinuation. The discourse segment C1. Adv1 C2

forms a complex constituent whose logical form,Continuation(F1, F2), is the second argumentof Explanation. So the discourse structure isExplanation(F0, Continuation(F1, F2)), which cor-responds to a tree-shaped dependency dag, seethe adjacent figure with R1 = Explanation andR2 = Continuation. In this example, the seconddiscursive argument of the conjunction because crossesa sentence boundary.

F1

R1

F0 R2

F2

In (1b), Adv2 = ε lexicalizes Explanation.The discourse structure is Explanation(F0, F1) ∧Explanation(F1, F2), which corresponds to a non tree-shaped dependency dag.

F1

R1

F0

R2

F2

In (1c), Adv2 = then lexicalizes Narration.The discourse structure is Explanation(F0, F1) ∧Narration(F0, F2), which corresponds to a non tree-shaped dependency dag. F1

R1

F0

R2

F2

In (1d), Adv2 = ε lexicalizes Commentary.The discourse segment C0 because C1 forms a com-plex constituent whose logical form is the first argu-ment of Commentary. So the discourse structure isCommentary(Explanation(F0, F1), F2), which corre-sponds to a tree-shaped dependency dag.

F1

R1

F0

R2

F2

In conclusion, these empirical data show that a formalism for the automatic anal-ysis of discourse must be able to compute dependency structures which are not

2 In [13], these four types of interpretation are finally brought to light, thanks to thePenn Discourse Tree Bank (PDTB), which is an English corpus manually annotatedfor discourse relations and their arguments [18].


tree-shaped.3 This principle guided the conception of d-stag. More precisely,from this (and other) data, we laid down the constraints below which governthe arguments of a discourse connective/relation using the following terminol-ogy. The clause in which a connective appears is called its “host clause”. Anadverbial connective appears in front of its host clause or within its VP. A sub-ordinating conjunction always appears in front of its host clause, which is calledan “adverbial clause.” At the sentence level, an adverbial clause modifies a “ma-trix clause.” It is located on its right, on its left, or inside it before its VP. Whenit is located on its right, the subordinating conjunction is said to be “postposed,”otherwise it is said to be “preposed.” A discourse connective/relation has twoarguments which are the syntactic/semantic representations of two discourse seg-ments that we call the “host segment” and the “mate segment”. These segmentsare governed by the following constraints.

Constraint 1. The host segment of a connective is identical to or starts at itshost clause (possibly crossing a sentence boundary).

Constraint 2. The mate segment of an adverbial is anywhere on the left of itshost segment (generally crossing a sentence boundary).4

Constraint 3. The mate segment of a postposed conjunction is on the left ofits host segment without crossing a sentence boundary.

Constraint 4. The mate segment of a preposed conjunction is identical to orstarts at the matrix clause (possibly crossing a sentence boundary).

3 Introduction to TAG and STAG

This section is reproduced except where noted from [17] with permission of theauthors. It begins with a brief introduction to the use of tag in syntax.

“A tree-adjoining grammar (tag) consists of a set of elementary tree struc-tures and two operations, substitution and adjunction, used to combine thesestructures. The elementary trees can be of arbitrary depth. Each internal nodeis labeled with a nonterminal symbol. Frontier nodes may be labeled with eitherterminal symbols or nonterminal symbols and one of the diacritics ↓ or ∗. Useof the diacritic ↓ on a frontier node indicates that it is a substitution node. Thesubstitution operation occurs when an elementary tree rooted in the nontermi-nal symbol A is substituted for a substitution node labeled with the nonterminalsymbol A. Auxiliary trees are elementary trees in which the root and a frontiernode, called the foot node and distinguished by the diacritic ∗, are labeled withthe same nonterminal. The adjunction operation involves splicing an auxiliary3 In rst, (1b) and (1c) are represented as trees that must be interpreted with the ”Nu-

clearity Principle” [16]. However, as explained in [7], the Nuclearity Principle leads toa wrong interpretation for (1d), namely Explanation(F0, F1)∧Commentary(F0, F2).

4 However, the mate segment must conform to the Right Frontier Constraint, whichhas been postulated in sdrt, see Sect. 5.1.

68 L. Danlos

P

NP↓ VP

V

likes

NP↓NP

John

=⇒P

NP

John

VP

V

likes

NP↓

P

NP↓ VP

V

likes

NP↓VP

Adv

apparently

VP*

=⇒P

NP↓ VP

Adv

apparently

VP

VP

likes

NP↓

Fig. 1. Example TAG substitution and adjunction operations (reproduced from [17])

NP

John

e

john

NP

Mary

e

mary

VP

Adv

apparently

VP∗

t

〈t, t〉

apparently

t∗

S ➀

NP↓ ➂ VP ➁

V

likes

NP↓ ➃

t ➀➁

〈e, t〉

〈e, 〈t, t〉〉

likes

e↓ ➃

e↓ ➂

Fig. 2. An English syntax/semantics stag fragment (reproduced from [17])

tree with root and designated foot node labeled with a nonterminal A at a nodein an elementary tree also labeled with nonterminal A. Examples of the sub-stitution and adjunction operations on sample elementary trees are shown inFigure 1.”

“Synchronous tag (stag) extends tag by taking the elementary structuresto be pairs of tag trees with links between particular nodes in those trees. Anstag is a set of triples, 〈tL, tR, �〉 where tL and tR are elementary tag trees and� is a linking relation between nodes in tL and nodes in tR [21,22]. Derivation


likes

johnapparently

mary

➂ ➃➁

S

NP

John

VP

Adv

apparently

VP

V

likes

NP

Mary

t

〈t, t〉apparently

t

〈e, t〉〈e, 〈e, t〉〉

likes

e

mary

e

john

Fig. 3. Derivation tree and derived tree pair for John apparently likes Mary (reproducedfrom [17] )

proceeds as in tag except that all operations must be paired. That is, a tree canonly be substituted or adjoined at a node if its pair is simultaneously substitutedor adjoined at a linked node.” We notate the links by using circled indices (e.g.➀) marking linked nodes.

stag has been successfully used in an English sentential syntax/semanticsinterface [17]. For the sentence John apparently likes Mary, Fig. 2 gives the stagfragment, Fig. 3 the derivation tree and the derived tree pair. In derivation trees,“substitutions are notated with a solid line and adjunctions are notated with adashed line. Note that each link in the derivation tree specifies a link numberin the elementary tree pair. The links provide the location of the operationsin the syntax tree and in the semantics tree. These operations must occur atlinked nodes in the target elementary tree pair. In this case, the noun phrasesJohn and Mary substitute into likes at links ➂ and ➃ respectively. The wordapparently adjoins at link ➁. The resulting semantic representation can be readoff the derived tree by treating the leftmost child of a node as a functor andits siblings as its arguments. Our sample sentence thus results in the semanticrepresentation apparently(likes(john, mary)).”

4 Sentence-Discourse Interface

We first explain why this interface is necessary. The idea in d-stag is to extenda sentential analyzer to the discourse level without making any change toit. Yet, one cannot directly pass from sentence to discourse because there aremismatches between the arguments of a connective at the discourse level and itsarguments at the sentence level. First, an adverbial connective has compulsorilytwo arguments at the discourse level, whereas it has only one argument at thesentence level. Second, a subordinating conjunction can have an argument atthe discourse level which crosses a sentence boundary (see (1a) and (3) below),whereas this is out of the question at the sentence level.

70 L. Danlos

In conclusion, it is necessary to pass through a sentence-discourse interfacewhich gives sentence boundaries the simple role of punctuation signs and whichallows us to re-compute the (two) arguments of a connective. Such an interfaceis also used in d-ltag, by which we were inspired. From the sentential syntacticanalysis, this interface deterministically produces a “Discourse Normalized Form”(henceforth dnf), which is a sequence of “discourse words:” a discourse word ismainly a connective, an identifier Ci for a clause (without any connective) or apunctuation sign. The syntactic and semantic analyses for Cis are those obtainedby the sentential analyzer by removing connectives. An adverbial connective ismoved in front of its host clause if not already there, while keeping a trace ofits original position. If a normalized sentence (except the very first one) doesn’tstart with an adverbial connective, the empty connective ε is introduced. As anillustration, for (2), the dnf is C0. ε as C1, C2. theninternal C3 because C4.

(2) Fred went to the movies. As he was in a bad mood, he didn’t enjoy it. Hethen went to a bar because he was dead thirsty.

The sequence of discourse words making up a dnf follows a regular grammar.In Section 5.1 dedicated to adverbial connectives and postposed conjunctions,a dnf follows the regular expression C (Punct Conn C)∗, in which the se-quence Punct Conn is either . Adv or (, ) Conj where the comma is optional.Disregarding punctuation signs, the dnf is: C0 Conn1 C1 . . . Connn Cn , withConni = Advi ou Conji. A dnf with a preposed conjunction (Sect. 5.2) includesone element C which is preceded by the expressions Conj C((, ) Conj C)∗. Con-nectives can be optionally followed or preceded by a modifier (Sect. 5.3). Coor-dinating conjunctions are studied in Section 5.4. Cases of “multiple connectives”in which two connectives share the same host clause are studied in Section 6.

This regular grammar doesn’t decompose clauses into sub-clauses: it takes intoaccount neither clausal complements nor incident clauses nor relative clauses,while these sub-clauses may play a role at the discourse level. We plan to com-plete the regular grammar for dnfs in future research and to extend the discur-sive component of d-stag accordingly (Sect 7).

5 Discursive Component of D-STAG

For a clause Ci (without any connective), the sentential-discourse interface pro-vides its syntactic tree rooted in S and noted Ti, its semantic tree rooted in t andnoted Fi, and its derivation tree noted τi. To plug the clausal analyses into thediscourse ones, we use the pair αS-to-D given in Fig. 4-a, in which the symbolDU represents the category “discourse unit”. In the rest of this paper, we noteηi the derivation tree made of αS-to-D in which τi is substituted at link �; ηi

corresponds to the pair given in Fig. 4-b. We also use the following convention:as any tree of our grammar includes at the most one substitution node, this one(when it exists) is systematically marked with link �.

When a given connective Conni lexicalizes a single discourse relation Ri, thebasic principle of the discursive stag grammar consists in designing a tree pair,


DU ➀

S↓ �

t ➀

t↓ �

(a) αS-to-D

DU ➀

Ti

t ➀

Fi

(b) ηi

Fig. 4. Tree pairs αS-to-D and ηi

noted Conni ÷ Ri, whose syntactic tree is anchored by Conni and whose se-mantic tree is anchored by a lambda-term associated with Ri. We say, althoughsomewhat inaccurately, that the semantic tree is anchored by Ri. When a con-nective is ambiguous, i.e. it lexicalizes several discourse relations, it anchors asmany syntactic trees as discourse relations it lexicalizes (this is in particular thecase for the empty connective ε). However, ambiguity issues are not in the scopeof this paper.

We start with the presentation of the stag discursive grammar for adverbialsand postposed conjunctions, which are connectives with a similar behavior.

5.1 Adverbial Connectives and Postposed Conjunctions

Syntactic trees. The syntactic trees anchored by an adverbial connective or bya postposed conjunction are given in Fig. 5, in which a discourse connective isof category DC. Disregarding the features for now, these trees differ only in theco-anchors which are punctuation signs of category Punct.

DU ➃[

t: -b: conj − post = −

]

DU ➂[

t: -b: conj − post = −

]

DU* Punct

.

DC

Advi

DU ➁

DU↓ �

DU ➃

DU ➂

DU*[

t: conj − post = +b: -

](Punct)

,

DC

Conji

DU ➁

DU↓ �

Fig. 5. Syntactic trees for adverbial connectives and postposed conjunctions

These trees observe the following principles: they are auxiliary trees withtwo arguments given by a substitution node DU↓ and a foot node DU∗. Thesubstitution node is for the host argument of the connective, i.e. the DU for thehost segment substitutes at DU↓. If the DU for the host clause has undergonean adjunction, then the host segment starts at — but is not identical to —the host clause, see Constraint 1 in Sect. 2. The foot node corresponds to themate argument of the connective. It is located on its left, which conforms toConstraints 2 and 3. The fact that the mate segment of a postposed conjunction

72 L. Danlos

cannot cross a sentence boundary, contrarily to that of an adverbial, is handledwith features [conj − post = ±] explained later.

We postulate an incremental analysis procedure in which the sequence ofthe discourse words of a dnf of the form C0 Conn1 C1 . . . Connn Cn (dis-regarding punctuation signs) is analyzed from left to right. After analyzingC0 . . . Connn Cn, the attachment of the new connective Connn+1 is realizedby adjunction of the tree anchored by Connn+1 at a node DU on the rightfrontier of the syntactic tree representing C0 . . . Connn Cn. The attachment ofthe new clause Cn+1 is realized by substituting the syntactic tree of the pair ηn+1

at the substitution node DU↓ of the tree anchored by Connn+1. Let us underlinethat this incremental procedure doesn’t take into account the segmentation ofthe discourse into sentences.

Trees anchored by an adverbial or a postposed conjunction include three nodeslabelled DU, with link ➁, ➂ or ➃, on their right frontier. These nodes are markedwith different links, which allows us to get various semantic interpretations, asshown below. There exist three nodes DU with different links, and not a singlenode DU with three different links, so as to allow several adjunctions to differentnodes, for example an adjunction at DU➂ to attach Connn and an adjunctionat DU➃ to attach Connn+1. It should be noted that if an adjunction is done atDU➂ to attach Connn, DU➁ is no longer on the right frontier of the syntactictree. Therefore, DU➁ can no longer be an adjunction site to attach Connn+1.This constraint will be generalized in Constraint 5 below.

Semantic trees. At first sight, one could consider that a discourse relation Ri

is associated with the functor Ri = λxy.Ri(x, y) with x, y : t, Ri(x, y) : t,and Ri : 〈t, 〈t, t〉〉, Ri anchoring a tree with a foot node t∗ and a substitutionnode t↓. Yet this is appropriate only to analyze a simple dnf with two clauses,for example a dnf of the form C0 because C1 as shown in Fig. 6 in whichβ1 = becausepost ÷ Explanation.

η1

β1

η0

�

➀t ➃

〈t, t〉

〈t, 〈t, t〉〉

R1

t

F0

t ➀

F1

R1 = ExplanationDU ➃

DU ➂

DU

T0

DC

because

DU ➁

DU ➀

T1

Fig. 6. Derivation tree and derived tree pair for a dnf of the form C0 because C1 (usingthe functor R1 in the semantic tree)

However, with this simple functor Ri, it is impossible to obtain four interpre-tations (of which two are a conjunction of formulae) for dnfs with three clauses(see Sect. 2). Therefore, we define two type-shifting operators Φ′ and Φ′′: they


take Ri as argument and return two new functors R′i and R′′

i associated withthe discourse relation Ri. Below the definitions.

Definition 1. Φ′ = λRiXY.X(λx.Y (λy.Ri(x, y)))Φ′(Ri) = R′

i = λXY.X(λx.Y (λy.Ri(x, y)))with X, Y : ttt = 〈〈t, t〉, t〉 and x, y : t

Φ′ triggers a type raising on the arguments. The resulting functor R′i is of type

〈ttt, 〈ttt, t〉〉 in which ttt symbolizes the type 〈〈t, t〉, t〉. It co-anchors tree (A),given in Fig. 7-a, whose foot node is of type t. (A) is used for adjunctions atlinks ➀ and ➃. If the first argument of R′

i is λP.P (F0) of type ttt, the secondone λQ.Q(F1) of type ttt, then the result is Ri(F0, F1) of type t. So, for a dnfwith two clauses, R′

i leads to the same result as Ri. Yet, the type raising isnecessary to introduce nodes ttt ➁ and ttt ➂ at which (B) can adjoin.

Definition 2. Φ′′ = λRiXY P.X(λx.Y (λy.Ri(x, y) ∧ P (x)))Φ′′(Ri) = R′′

i = λXY P.X(λx.Y (λy.Ri(x, y) ∧ P (x)))with X, Y : ttt = 〈〈t, t〉, t〉, P : 〈t, t〉 and x, y : t

Φ′′ introduces a conjunction of terms. The resulting functor R′′i is of type

〈ttt, 〈ttt, ttt〉〉. It anchors tree (B), given in Fig. 7-b, whose foot node is of typettt. (B) is used for adjunctions at links ➁ and ➂. If the first argument of R′′

i isλP.P (F0), the second one λQ.Q(F1), then the result is λP.(Ri(F0, F1) ∧ P (F0))of type ttt.

Analysis of dnfs with three clauses. For dnfs with three clauses, four types ofinterpretation must be computed. These were illustrated in examples (1) of theform C0 because C1. Adv2 C2 in Sect. 2, and we are going to explain the analysisof these examples. We call β1 the tree pair becausepost÷Explanation and β2 thepair Adv2 ÷R2. After analyzing C0 because C1, the syntactic tree is that shownin Fig. 6. The right frontier of this tree includes four nodes labelled DU whichcan receive the adjunction of the syntactic tree of β2. These nodes are markedwith link ➀ coming from the syntactic tree of η1 or link ➁, ➂ or ➃ coming fromthe syntactic tree anchored by because. The analyses of the four examples in (1)are obtained by adjoining β2 at one of these links.

We start with (1a) with β2 = moreover ÷ Continuation, for which the dis-course structure is Explanation(F0, Continuation(F1, F2)). This is obtained byadjoining β2 at link ➀ of η1. The node with link ➀ in the semantic tree of η1

is of type t. Therefore, one must use tree (A) anchored by R′2, whose foot node

is of type t. The semantic derived tree for (1a) is given in Fig. 8. The sub-treerooted at Gorn address 2 results in λP.P (Continuation(F1, F2)) with P : 〈t, t〉.So Continuation(F1, F2) is the second argument of R1 = Explanation, whosefirst argument is F0, hence the formula Explanation(F0, Continuation(F1, F2)).

We go on with (1b) with β2 = ε ÷ Explanation, for which the discoursestructure is Explanation(F0, F1) ∧ Explanation(F1, F2) with a conjunction offormulae. This is obtained by adjoining β2 at link ➁ of β1. The node withlink ➁ in the semantic tree of β1 is of type ttt. Therefore, one must use tree

74 L. Danlos

〈ttt, t〉

〈ttt, 〈ttt, t〉〉

〈. . .〉

Φ′

〈t, 〈t, t〉〉

Ri

ttt ➂

λ P t

P t∗

ttt ➁

λ Q t

Q t↓�

t ➃

(a) Tree (A)

〈ttt, ttt〉

〈ttt, 〈ttt, ttt〉〉

〈. . .〉

Φ′′

〈t, 〈t, t〉〉

Ri

ttt ➂

ttt∗

ttt ➁

λ Q t

Q t↓�

ttt ➃

(b) Tree (B)

Fig. 7. Semantic trees (A) and (B) anchored by R′i = φ′(Ri) and R′′

i = φ′′(Ri)

(B) anchored by R′′2 , whose foot node is of type ttt. The semantic derived tree

for (1b) is given in Fig. 9-a. The sub-tree rooted at Gorn address 2 results inλP.(Explanation(F1, F2) ∧ P (F1)) with P : 〈t, t〉. As only F1 is under P , it isthe second argument of R1 = Explanation, whose first argument is F0, hencethe formula Explanation(F0, F1) ∧ Explanation(F1, F2).

For (1c) with β2 = then÷Narration, the structure is Explanation(F0, F1)∧Narration(F0, F2) with also a conjunction of formulae. This is obtained by ad-joining β2 at link ➂ of β1. This case is similar to the previous one, so we simplygive the semantic derived tree in Fig. 9-b.

Let us finish with (1d) with β2 = ε ÷ Commentary, for which the structureis Commentary(Explanation(F0, F1), F2). This is obtained by adjoining β2 atlink ➃ of β1. The node with link ➃ in the semantic tree of β1 is of type t.Therefore, one must use tree (A) anchored by R′

2. The semantic derived treefor (1d) is given in Fig. 10. The sub-tree rooted at Gorn address 1.2 results inλP.P (Explanation(F0, F1)) with P : 〈t, t〉.

In conclusion, the four types of interpretation of dnfs of the form C0 Conj1 C1.Adv2 C2 are computed thanks to the four adjunction sites on the right frontier ofthe syntactic tree for C0 Conj1 C1 and to semantic trees (A) and (B) whose footnodes are respectively of type t et ttt and which are anchored by R′

i and R′′i .

For dnfs with three clauses of the form C0 Conn1 C1 Conn2 C2, we havejust examined the case C0 Conj1 C1. Adv2 C2 where Conn1 is a postposedconjunction and Conn2 an adverbial. Three cases are left: Conn1 is a postposed


t

〈ttt, t〉


R′1

ttt

λP.P (F0)

ttt

λ P t

P t

〈ttt, t〉


R′2

ttt

λQ.Q(F1)

ttt

λS.S(F2)

R1 = Explanation

R2 = Continuation

Fig. 8. Semantic derived tree for (1a) with interpretation R1(F0, R2(F1, F2))

conjunction and Conn2 also, Conn1 is an adverbial and Conn2 also, Conn1 is anadverbial and Conn2 a postposed conjunction. The first two cases raise no newissues. The third case, which concerns dnfs of the form C0. Adv1 C1 Conj2 C2,raises the issue of fully implementing Constraint 3 from Sect. 2, which states thatthe mate segment of a postposed conjunction cannot cross a sentence boundary.This constraint is implemented thanks to features [conj − post = ±] which deco-rate some nodes in the syntactic trees anchored by an adverbial or a postposedconjunction, which are given in Fig. 5. More precisely:

– the foot node of a tree anchored by a postposed conjunction is decoratedwith the top feature conj − post = +,

– the nodes with links ➂ and ➃ in a tree anchored by an adverbial are decoratedwith the bottom feature conj − post = −.

These features block the adjunction of Conj2÷R2 at links ➂ and ➃ of Adv1÷R1

thanks to unification failure (conj − post = +) ∪ (conj − post = −). There-fore, Conj2 ÷ R2 can only adjoin at link ➁ of Adv1 ÷ R1 and at link ➀ ofη1, which results respectively in interpretations R1(F0, F1) ∧ R2(F1, F2) andR1(F0, R2(F1, F2)). These interpretations conform to Constraint 3: the mateargument of R2 is F1, so the mate segment of Conj2 is C1, which doesn’t crossa sentence boundary.

Analysis of dnfs with n clauses (n > 3) of the form C0 Conn0 C1 . . . Cn.For dnfs with n clauses, no new mechanism is involved. Attaching Connn+1

next Cn+1 consists, in the derivation tree representing C0 . . . Cn, in adjoiningConnn+1 ÷ Rn+1 — in which ηn+1 is substituted — at link ➀ of ηn or at link

i with i ∈ {2, 3, 4} of a node βk = Connk ÷ Rk, the node at link i comingfrom the syntactic tree of βk being on the right frontier of the syntactic treefor C0 . . . Cn (to keep to the linear order of the dnf). As it is long and tedious

76 L. Danlos

t

〈ttt, t〉


R′1

ttt

λP.P (F0)

ttt

〈ttt, ttt〉


R′′2

ttt

λQ.Q(F1)

ttt

λS.S(F2)

(a) (1b) with R1 = R2 = Explanation

t

〈ttt, t〉


R′1

ttt

〈ttt, ttt〉


R′′2

ttt

λP.P (F0)

ttt

λQ.Q(F2)

ttt

λS.S(F1)

(b) (1c) with R1 = Explanation and R2 = Narration

Fig. 9. Semantic derived trees for (1b) and (1c) with interpretations R1(F0, F1) ∧R2(F1, F2) and R1(F0, F1) ∧ R2(F0, F2)

t

〈ttt, t〉


R′2

ttt

λ P t

P t

〈ttt, t〉


R′1

ttt

λP.P (F0)

ttt

λQ.Q(F1)

ttt

λS.S(F2)

R1 = ExplanationR2 = Commentary

Fig. 10. Semantic derived trees for (1d) with interpretation R2(R1(F0, F1), F2)

to determine (the right frontier of) the derived syntactic tree, it is convenientto define a notion of right frontier on the derivation tree. Since derivation treesare intrinsically not ordered, a graphical convention which represents derivationtrees as ordered must be called upon. The following convention is satisfactory:


the nodes labeled ηk projected onto a line are ordered by following the linearorder of the dnf. With this order relation noted ≺, the nodes βk in the derivationtree which are possible sites of adjunction for a new segment are those on theright frontier of the derivation tree, while observing Constraint 5 which governstwo adjunctions at links n and m of the same node:5

Constraint 5. If βj — in which ηj is substituted — adjoins at link n of anode βi, then βk — in which ηk is substituted — can adjoin at link m of thesame node βi only if the following rule is observed: ηj ≺ ηk ⇒ n < m (with nand m belonging to {2, 3, 4}).This constraint generalizes the one we formulated before, namely, if an adjunc-tion is performed at node DU➂ of a syntactic tree anchored by Conni, then anew adjunction in this tree can be performed at DU➃ but not at DU➁.

Implementation of RFC. The Right Frontier Constraint (RFC) postulated insdrt relies on a distinction between two types of discourse relations: coordinating(Narration, Continuation) versus subordinating (Explanation, Commentary)ones. RFC says that it is forbidden to attach new information to the first argu-ment of a coordinating relation [2]. As a consequence, for example, the interpre-tation R1(F0, F1) ∧ R2(F0, F2) is excluded when R1 is coordinating.

Implementing RFC in d-stag requires first to distinguish the semantic treesanchored by a coordinating versus subordinating relation. This is achieved bycreating two copies of semantic trees (A) and (B), which differ in a top feature[coord = ±] decorating their foot node. Then RFC is implemented by forbiddingany adjunction at link ➂ of the copies of (A) and (B) whose foot node is decoratedwith the feature [coord = +]: it is link ➂ which is used to obtain interpretationslike R1(F0, F1) ∧ R2(F0, F2) which must be excluded when R1 is coordinating.

sdrt postulates other semantic constraints based on the distinction betweencoordinating versus subordinating relations, for example the “Continuous Dis-course Pattern” [3]. There is no room to describe them, however we can say thatthey are easily implemented in d-stag thanks to the addition of a set of featuresin the semantic trees.

5.2 Preposed Conjunctions

The syntactic tree anchored by a preposed conjunction is given in Fig. 11. It isdesigned so as to respect Constraints 1 and 4 given in Sect. 2. It differs fromthe syntactic trees anchored by an adverbial or a postposed conjunction, amongother things, by the fact that the foot node DU∗ is dominated by a node DUwith link ➄. To take into account this new link, a node t➄ dominating the footnode t∗ is added into the two copies of semantic tree (A).

An adjunction to link ➄ is used when the preposed conjunction introduces a“framing adverbial” [4] as illustrated in (3) of the form When C0, C1. Next C2. In

5 This constraint is valid because we assigned links ➁, ➂ and ➃ in a well-thought-outmanner.

78 L. Danlos

DU ➃

DU ➂

DC

Conji

DU ➁

DU↓ �

Punct

,

DU ➄

DU*

whenpre ÷ Circumstance

η1

η0 next ÷ Narration

η2

➀

� ➄

�

Fig. 11. Tree anchored by a preposed conjunction and derivation tree for (3)

this discourse, the preposed conjunction when has its mate segment which crossesa sentence boundary. Its interpretation is Circumstance(Narration(F1, F2), F0),assuming that when conveys Circumstance and next conveys Narration.

(3) When he was in Paris, Fred went to the Eiffel Tower. Next, he visited TheLouvre.

The derivation tree for (3) is given in Fig. 11. The semantic trees anchored byCircumstance and Narration are both (A). The arguments of the functor asso-ciated to Circumstance are λP.P (Narration(F1 , F2)) and λQ.Q(F0). Therefore,Narration(F1, F2) is the first argument of Circumstance, F0 the second one.6

5.3 Modifiers of Discourse Connectives/Relations

As far as we are aware, modification of discourse connectives/relations is a phe-nomenon which has been neglected. However, it is a common phenomenon asillustrated in (4).

(4) a. Fred is in a bad mood only/even/except when it is sunny.b. You shouldn’t trust John because, for example, he never returns what he

borrows. [23]c. John just broke his arm. So, for example, he can’t cycle to work.[23].

In [23], for example is not considered as a connective modifier but as a connectivewhose interpretation is “parasitic” on the relation conveyed by the connectiveon its left. This position, which is not linguistically justified, leads to laboriouscomputations in d-ltag [10, pp 31-35] to obtain the interpretation of (4b). Onthe contrary, in d-stag, we propose that for example in (4b) or (4c) is a modifierof the connective on its left in the same way that only, even and except in (4a)are modifiers of the connective on their right. This position sounds more justifiedon linguistic grounds and it allows us to obtain the interpretation of a discoursesuch as (4b) in a very simple way, as we are going to show.

6 Examples such as (3) make it that, despite appearances, the syntactic discursivegrammar of d-stag is not a tig (Tree Insertion Grammar) [20], since the right treeanchored by next is adjoined on the spine of the left tree anchored by the preposedconjunction when.


DC

DC∗ for example

〈t, 〈t, t〉〉

〈. . . 〉

For-ex

〈t, 〈t, t〉〉∗

η0

becausepost ÷ Explanation

βfor-exη1

➀

➅�

Fig. 12. Pair βfor-ex and derivation tree for (4b)

In d-stag, connective modifiers anchor (syntactic) auxiliary trees whose footnode is DC (left tree for only, even and except, right tree for for example).To adjoin these trees, we mark the node labelled DC with link ➅ in the syn-tactic trees for connectives (Fig. 5 and 11). At the semantic level, we assumethat the contribution of a discourse relation modifier consists in transforminga functor Ri of type 〈t, 〈t, t〉〉 into another functor of the same type. There-fore, the nodes dominating Ri are marked with link ➅ in the two copies of(A) and (B). Let us illustrate adjunctions to link ➅ with (4b) of the formC0 because for example C1. As explained in [23], the interpretation of (4b)is Exemplification(F1, λr.Explanation(F0, r)) with r : t. To get this inter-pretation, we define the functor For-ex as below. The pair named βfor-ex isgiven in Fig. 12, which also shows the derivation tree for (4b). The functorΦ′(For-ex (Ri)) with Ri = Explanation results in the right interpretation.

Definition 3. For-ex = λRipq.Exemplification(q, λr.Ri(p, r))with Ri : 〈t, 〈t, t〉〉 and p, q : t.

5.4 Coordinating Conjunctions

For reasons that will be obvious later, we start with correlative coordinations ofadverbial clauses, which are illustrated in (5). These correlative coordinationscan easily be handled in d-stag by considering e.g. neither and nor as (adver-bial) modifiers of the subordinating conjunction on their right. The correlativepart of these constructions, e.g. the fact that neither cannot modify a subordinat-ing conjunction without the presence of either modifying another subordinatingconjunction, is taken into account by a set of features in the syntactic treesanchored by a subordinating conjunction (there is no room to explain these fea-tures). This set of features also forces the adjunction of the tree anchored bythe second (modified) subordinating conjunction to link ➂ of the tree anchoredby the first (modified) subordinating conjunction. As a result, the interpretationis a conjunction of formulae in which the logical form of the matrix clause isshared. More precisely, for (5a) of the form C0 neither when C1 nor when C2,the interpretation ¬Condition(F0, F1) ∧ ¬Condition(F0, F2) — assuming thatwhen lexicalizes the relation Condition — is obtained (through an adjunctionof the second when at link ➂ of the first when) by giving neither and nor the

80 L. Danlos

semantics of negation. For (5b) of the form C0 either if C1 or if C2, the in-terpretation Condition(F0, F1) ∨ Condition(F0, F2) = ¬(¬Condition(F0, F1) ∧¬Condition(F0, F2)) is obtained by giving to or the semantics of negation andby associating to either a semantic tree with two parts, one for the local scopeof negation, the other one for the global scope of negation over the conjunctionof formulae.7 For (5c) of the form C0 both when C1 and when C2, the interpre-tation Condition(F0, F1) ∧ Condition(F0, F2) is obtained by giving to both andand the semantics of identity.

(5) a. Fred is pleased neither when it is sunny nor when it is rainy.b. Fred will come either if it is sunny or if it is rainy.c. Fred is pleased both when it is sunny and when it is rainy.

We now examine non-correlative coordinations. Coordinations of two matrixclauses with a dnf of the form C0 Coord1 C1 are handled with a syntactic treeanchored by the coordinating conjunction Coord1 similar to the syntactic treeanchored by a subordinating conjunction (Fig. 5). Coordination of n clauses withn > 2 with a dnf of the form C0, C1(, ) Coord2 C2 are handled with the stan-dard mechanisms for multiple coordinations. Coordinations of adverbial clauseswith a dnf of the form C0 Conj1 C1 or/and Conj2 C2 raise drastic problems, inparticular to get their interpretation. However, it must be noted that the inter-pretation of (5b)/(5c) doesn’t change if either/both is omitted. In other words, anon-correlative coordination of adverbial clauses is semantically equivalent to acorrelative coordination. Therefore, we propose that the sentence-discourse inter-face automatically converts a non-correlative coordination of adverbial clausesinto a correlative one, e.g. converts the dnf C0 Conj1 C1 or Conj2 C2 into thednf C0 either Conj1 C1 or Conj2 C2 that we can handle by considering eitherand or as modifiers of the subordinating conjunction on their right.

6 Comparison between D-STAG and D-LTAG

d-stag and d-ltag [10] roughly share the same goal and the same architecture.The discrepancies between these two formalisms mainly lie in the discursivecomponent.8 First, d-ltag makes little use of discourse relations and ignoresthe distinction between coordinating versus subordinating relations. In short, itdoesn’t build on discourse theories. This is even a principle, as shown in thequotation [10, p 1] “ d-ltag presents a model of low-level discourse structureand interpretation that exploits the same mechanisms used at the sentence leveland builds them directly on top of clause structure and interpretation”. Thisprevents d-ltag from taking advantage of the insights provided by discoursetheories, which supply rhetorical knowledge, among other things.7 This is the only case which requires a multi-component semantic tree.8 The sentential components of d-stag and d-ltag are also crucially different, since

d-stag relies on stag, which is not the case for d-ltag. However, the sentential levelis out of the scope of this paper, see [17] for a discussion on the various approachesfor a sentential syntax-semantics interface.


DU

DC

ε

DU

DU

T0

DC

because

DU

T1

DU

DC

then

DU

T2

αbecause

η0 η1

βε

η2

βthen

Fig. 13. d-ltag syntactic tree and derivation tree for (1c) = Fred went to the super-market because his fridge is empty. Then, he went to the movies.

Next, discourse connectives in d-stag all anchor elementary trees with twoarguments, whereas, in d-ltag, most adverbial connectives (but not the emptyone ε) anchor trees with only one argument (this is, for example, the case forthen whose host segment is “structurally” provided, the mate segment being“anaphorically” provided [23]). Moreover, subordinating conjunctions in d-ltaganchor trees with two arguments, but these trees are initial trees whereas theyare auxiliary in d-stag (subordinating conjunctions are considered in d-ltagas “structural” connectives, neglecting the fact that one of their segments cancross a sentence boundary, (1a) and (3)). These discrepancies between the treesanchored by a connective lead to crucial differences in the discursive analyses,especially in the semantic ones.

As an illustration, the syntactic tree and derivation tree produced by d-ltagfor (1c) are given in Fig. 13. The syntactic tree includes three nodes labelled DC,while it includes only two nodes labelled DC in d-stag since the empty connec-tive ε is introduced only in the absence of any other adverbial. The derivation treeresults in the discourse structure Narration(Explanation(F0, F1), F2), which iswrong: the explanation given for Fred’s visit to the supermarket (his fridge wasempty) shouldn’t be under the scope of Narration, which is a relation linking to-gether two events and not a causal relation and an event. As explained in Sect.2,the discourse structure for (1c) is Explanation(F0, F1)∧Narration(F0, F2). Thisstructure, which corresponds to a non tree-shaped dependency graph, cannot beobtained in d-ltag.

“Multiple connectives” is a phenomenon which guided the conception of d-ltag, as shown in the quotation [23, p 552]: “The distinction between structuraland anaphoric connectives in d-ltag is based on considerations of computationaleconomy and behavioral evidence from cases of multiple connectives”. The dis-course (6) gives an illustration of multiple connectives. Its dnf is of the formC0 but C1 because then C2, in which two connectives share the same host clauseC2, the second one being an adverbial.

(6) John ordered three cases of Barolo. But he had to cancel the order becausethen he discovered he was broke. [23]

In d-stag, we propose the following solution to handle multiple connectives. Thednf for (6) is automatically converted into C0 but C1 because C2 then C2 whichconforms to the regular pattern for dnfs (without any preposed conjunction).

82 L. Danlos

DU ➀

ε

t ➀

F2

(a) η2

η1

β1

η0

β2

η2

β3

η2

�

➀

➁

� �

➂

(b) Derivation tree for (6)

Fig. 14. Tree pair η2 and derivation tree for (6)

The tree pair η2 associated to C2 is given in Fig. 14-a: the syntactic leaf is theempty string ε, the semantic leaf is F2 (the semantic formula for C2). So we cansay that C2 is the (fake) host clause of because, which has only a semantic contri-bution. The interpretation of (6), i.e. Contrast(F0, F1)∧Explanation(F1, F2)∧Narration(F0, F2) assuming that then conveys Narration, is obtained by themechanisms described in Sect. 5.1.1 which build the derivation tree given inFig. 14-b (with β1 = but ÷ Contrast, β2 = because ÷ Explanation and β3 =then ÷ Narration).9

In conclusion, cases of multiple connectives can be boiled down to the generalpattern in which an host clause receives only a single connective, thanks tothe sentence-discouse interface (which in any case cannot be bypassed (Sect.4)).Therefore, there is no need to postulate a distinction between anaphoric andstructural connectives, the former with a single argument, the latter with twoarguments.

7 Conclusion

We focused on an stag discursive grammar for connectives/discourse relations.It aims at handling any type of connectives (adverbials, postposed and pre-posed subordinating conjunctions, coordinating conjunctions (including coordi-nating conjunctions in correlative constructions), any modifier of a connective,and finally cases of “multiple connectives”. The syntactic discursive grammarfor connectives shows that it is justified to postulate that any connective an-chors an auxiliary tree with two arguments: a foot node DU∗ for the mateargument , a substitution node DU↓ for the host argument which is identical toor starts at the host clause of the connective. The semantic discursive grammaris made up from trees anchored by functors associated to discourse relations,which are considered as predicates lexicalized by discourse connectives. It allowus to compute discourse structures which are not compulsorily represented astree-shaped dependency graphs.

9 The interpretation of (6) looks as a counter-example to RFC since the discourserelation Contrast is coordinating. However, we explain in [8] how to handle thisapparent counter-example.


The discursive component takes as input a dnf that is computed by a sentence-discourse interface. This interface is necessary if one doesn’t want to make anychange to the sentential analyzer. A dnf is a sequence of discourse words whichfollows a regular grammar. The regular grammar we have presented in this paperfocuses on connectives but is not yet completed. In particular, it doesn’t takeinto account sub-clauses (clausal complements, incident clauses, relative clauses)which may play a role at the discursive level. This is ongoing work [9] and wedon’t foresee any crucial difficulty for the resulting extended discursive grammar,thanks to stag’s richness of expressivity.

The implementation of d-stag in a French discourse analyzer is work inprogress [8]. The analyzer will produce a forest of derivation trees which repre-sents the set of possible analyses. The extraction of the best analysis (or the nbest analyses) will require to build probabilistic disambiguation models basedon the French annotated corpus Annodis [19].

References

1. Asher, N.: Reference to Abstract Objects in Discourse. Kluwer, Dordrecht (1993)

2. Asher, N., Lascarides, A.: Logics of Conversation. Cambridge University Press,Cambridge (2003)

3. Asher, N., Vieu, L.: Subordinating and coordinating discourse relations. Lin-gua 115(4), 591–610 (2005)

4. Charolles, M.: Framing adverbials and their role in discourse cohesion, from connec-tion to foward labelling. In: Proceedings of the First Symposium on the Explorationand Modelling of Meaning, SEM 2005, Biarritz, pp. 194–201 (2005)

5. Danlos, L.: A lexicalized formalism for text generation inspired from TAG. In:Abeille, A., Rambow, O. (eds.) TAG Grammar. CSLI, Stanford (2001)

6. Danlos, L.: Discourse dependency structures as constrained DAGs. In: Proceedingsof SIGDIAL 2004, Boston, pp. 127–135 (2004)

7. Danlos, L.: Strong generative capacity of RST, SDRT and discourse dependencyDAGs. In: Benz, A., Kuhnlein, P. (eds.) Constraints in Discourse, Benjamins (2007)

8. Danlos, L.: D-STAG: un formalisme d’analyse automatique de discours base surles TAG synchrones. Revue TAL 50(1), 111–143 (2009)

9. Danlos, L., Sagot, B., Stern, R.: Analyse discursive des incises de citations. In:Actes du Second Colloque Mondial de Linguistique Francaise New-Orleans, USA(submitted)

10. Forbes-Riley, K., Webber, B., Joshi, A.: Computing discourse semantics: Thepredicate-argument semantics of discourse connectives in D-LTAG. Journal of Se-mantics 23(1) (2006)

11. Harris, Z.: Mathematical Structures of Language. Krieger Pub. Co., New York(1986)

12. Joshi, A.: Tree-adjoining grammars. In: Dowty, D., Karttunen, L., Zwicky, A. (eds.)Natural Language Parsing, pp. 206–250. Cambridge University Press, Cambridge(1985)

13. Lee, A., Prasad, R., Joshi, A., Webber, B.: Departures from tree structures indiscourse: Shared arguments in the penn discourse tree bank. In: Proceedings ofthe Constraints in Discourse Workshop (CID 2008). Postdam, Germany (2008)

84 L. Danlos

14. Mann, W.C., Thompson, S.A.: Rhetorical structure theory: Toward a functionaltheory of text organization. Text 8(3), 243–281 (1988)

15. Marcu, D.: The rhetorical parsing of unrestricted texts: A surface-based approach.Computational Linguistics 26(3), 395–448 (2000)

16. Marcu, D.: The Theory and Practice of Discourse Parsing and Summarization. TheMIT Press, Cambridge (2000)

17. Nesson, R., Shieber, S.: Simpler TAG semantics through synchronization. In: For-mal Grammars, Malaga (2006)

18. PDTB Group: The penn discourse treebank 2.0 annotation manual. Tech. Rep.IRCS-08-01, Institute for Research in Cognitive Science, University of Philadelphia(2008)

19. Pery-Woodley, M.P., Asher, N., Enjalbert, P.: ANNODIS: une approche outillee del’annotation de structures discursives. In: Proceedings of TALN 2009, pp. 190–196.Senlis, France (2009)

20. Schabes, Y., Waters, R.: Tree insertion grammar. Computational Intelligence 21,479–514 (1995)

21. Shieber, S.: Restricting the weak-generative capacity of synchronous tree-adjoininggrammars. Computational Intelligence 10(4), 371–385 (1994)

22. Shieber, S., Schabes, Y.: Synchronous tree-adjoining grammars. In: Proceedings ofthe 13th International Conference on Computational Linguistics, vol. 3, pp. 253–258. Helsinki, Finland (1990)

23. Webber, B.L., Joshi, A., Stone, M., Knott, A.: Anaphora and discourse structure.Computational Linguistics 29(4), 545–587 (2003)

24. Wolf, F., Gibson, E.: Coherence in Natural Language: Data Structures and Appli-cations. The MIT Press, London (2006)

D-STAG: A Formalism for Discourse Analysis Based on SDRT ...

Documents

Transcript of D-STAG: A Formalism for Discourse Analysis Based on SDRT ...